If E, M, J and G respectively denote energy, mass, angular momentum and universal gravitational constant, the quantity, which has the same dimensions as the dimensions of (E J2/M5 G2)

Question

If E, M, J and G respectively denote energy, mass, angular momentum and universal gravitational constant, the quantity, which has the same dimensions as the dimensions of (E J2/M5 G2) (A) time (B) angle (C) mass (D) length

Tardigrade Admin · Accepted Answer

Given quantity is (E J2/M5 G2) ...(i) where dimensions of the various given quantities are Dimensions of E=[ ML 2 T -2] Dimensions of J=[ ML 2 T -1] Dimension of M=[ M ] Dimension of G=[ M -1 L 3 T -2] Now, on putting these dimensions in Eq. (i), we have =([ ML 2 T -2][ ML 2 T -1]2/[ M 5][ M -1 L 3 T -2]2) =([ M 3 L 6 T -2]/[ M 3 L 6 T -2])= dimensionless Since, angle is a dimensionless quantity

Q. If E,M,J and G respectively denote energy, mass, angular momentum and universal gravitational constant, the quantity, which has the same dimensions as the dimensions of M5G2EJ2​

time

angle

mass

length

Q. If $E, M, J$ and $G$ respectively denote energy, mass, angular momentum and universal gravitational constant, the quantity, which has the same dimensions as the dimensions of $\frac{E J ^{2}}{M ^{5} G ^{2}}$